It would be beneficial to take a look at the Zion Traverse. If you google it you will most likely come with some ultra running races and stuff, but it is awesome to backpack. Good distance for 3-4 days and Zion is seriously breathtaking. Some of the views are astonishing, namely Angels Landing.
Bryce is also beautiful, but I have not been there myself (only drooled over pictures). I have however been to Zion and cant wait to go back.
Just be sure to check with the backcountry permit desk at the park. You need to get permits from them to do the hike (should not be an issue as they reserve some for walk-ups if my memory serves me).